一类带有接种的流行病模型的全局稳定性

该文讨论了一类带有接种的流行病模型. 在该模型中假设恢复后的个体与被接种的个体均具有确定的免疫期, 它是一个时滞微分系统. 通过分析, 得到了地方病平衡点存在的阈值, 以及无病平衡点和地方病平衡点局部渐近稳定和全局渐近稳定的充分条件.     

灰色GM(1,1,k,k2)模型背景值及时间响应函数优化

本文提出了一种新的带有时间幂次项的灰色GM(1,1,k,k²)模型,给出了其灰微分方程和白化微分方程基本形式。基于最小二乘法获得了该模型参数估计值,并推导了该模型时间响应函数。鉴于GM(1,1,k,k²)模型灰微分方程与白化微分方程之间存在跳跃关系,首先对灰微分方程的背景值进行了优化,并推导了优化后的背景值计算公式。为了克服初始值的影响,根据误差平方和最小,进一步优化了GM(1,1,k,k²)模型时间响应函数。最后,该优化后的GM(1,1,k,k²)模型被应用于软土地基沉降预测,获得了较好的模拟预测效果,说明模型是可行的。     

耦合的Fitz-Hugh-Nagumo模型的初边值问题

首先研究了具有耦合的Fitz-Hugh-Nagumo模型初值问题的渐近性.其次,所对应的平衡态方程解的基本性态也将被讨论.最后,该模型的初边值问题古典解的最大吸引子的存在性将首次被证明.     

二叉树模型的参数估计

二叉树模型是期权定价中被广泛使用的模型之一, 其参数估计对于期权定价具有重要影响. 本文给出了一种二叉树模型参数估计方法, 该方法克服了二叉树模型经典参数估计方法的缺陷, 特别地, 消除了主观概率设定对参数估计的影响.     

含状态转换的Copula模型及其应用

Copula在金融资产风险分析中被广泛应用,本文考虑了一种含状态转换的Copula模型。该模型的特点是,Copula函数在一个状态内是固定的,在不同状态之间的转移过程是一个不可观测的马氏链。其不同的状态可以用来描述金融资产相关性的波动。我们运用该模型对我国股票市场进行了实证研究,结果表明该模型可以更好地衡量其相关性模式。     

非线性再生散度模型的Bayes估计

非线性再生散度模型是指数族非线性模型、广义线性模型和正态非线性回归模型的推广和发展,唐年胜等人研究了该模型参数的极大似然估计及其统计诊断。本文基于Gibbs抽样和MH抽样算法讨论非线性再生散度模型参数的Bayes估计。模拟研究和实例分析被用来说明该方法的有效性。     

均值-叉熵证券投资组合优化模型

在研究马科维茨(Markowitz)证券投资组合模型的基础上,分析了该模型用方差度量风险的缺陷,进而提出用叉熵作为风险的度量方法,建立了均值-叉熵的投资组合优化模型.该模型计算简便,更易被一般投资人所使用.     

耦合的Fitz-Hugh-Nagumo模型的初边值问题

首先研究了具有耦合的Ｆｉｔｚ－Ｈｕｇｈ－Ｎａｇｕｍｏ模型初值问题的渐近性．其次，所对应的平衡态方程 解的基本性态也将被讨论．最后，该模型的初边值问题古典解的最大吸引子的存在性将首次被证明．     

模糊T划分下基于贴近度的变精度粗糙模糊集模型

粗糙集模型的扩展是粗糙集研究的重要内容之一,根据论域中知识和被近似对象的特点,学者们提出了针对不同情况的粗糙集模型,如Pawlaw针对知识和被近似对象都是确定的,提出了经典粗糙集模型,dubois针对知识是确定的而被近似对象是模糊的情况提出了粗糙模糊集模型。而本文是在知识和被近似对象都是模糊的情况下建立了一个新的变精度模型,首先是将论域进行模糊T划分,得到论域上的各个模糊子集,然后根据模糊的被近似对象与论域上的模糊子集之间的贴进程度关系,得到了新的变精度粗糙模糊集模型,并且研究了算子的有关性质,最后举例说明了该模型的应用。     

考虑消费动机和动态竞争的电影日需求预测模型

提出并验证考虑消费动机和动态竞争的电影日需求预测模型。考虑非粉丝及粉丝型的消费动机,构建电影消费两阶段过程模型;融合该模型和Bass模型,考虑竞争导致市场潜量的动态性,考虑映前被关注度、口碑、节假日对票房的影响,提出电影日需求预测模型。利用2016~2017年上映的电影数据验证该模型,并与Bass模型对比分析。结果显示,该模型预测效果优于Bass模型。因考虑竞争导致的动态市场潜量,考虑粉丝型消费者由续集效应及改编效应导致的动态市场潜量提升,该模型能显著提高预测准确度。利用映前被关注度和电影口碑数据,该模型能实现映前及上映早期的预测。该模型可推广至存在消费动机不同、市场动态竞争的其它短生命周期体验品的需求预测,是对Bass模型的改进。     

Cobb—Douglas生产函数参数估计的加权方法

本文给出了Cobb-Douglas生产函数参数估计的加权方法,实例分析表明,本文方法所得模型的精度明显高于经典方法所得模型的精度。     

提高水分子流出纳米碳管速度的特殊水分子偶极排布研究

使用分子动力学的方法,研究了水分子进出狭窄碳纳米管的过程．发现管口处水分子的偶极垂直于碳管时容易流出碳管．根据碳管中与之相邻的水分子的偶极方向可以把这种特殊构型分为2类．虽然,这2类特殊结构的出现概率非常小,但是它们对净流过碳管水分子的贡献与其它结构的贡献基本相同．这2种偶极排布中水分子比较接近管壁、远离Lennard-Jones势的平衡位置,导致这2种偶极排布中水分子能量升高,处于相对不稳定的状态,容易流出碳管．这个发现表明可以通过调控碳纳米管内的水分偶极方向控制管内的水分子流动．     

Topological analysis of chaotic time series data from the Belousov-Zhabotinskii reaction

Summary We have applied topological methods to analyze chaotic time series data from the Belousov-Zhabotinskii reaction. First, the periodic orbits shadowed by the data set were identified. Next, a three-dimensional embedding without self-intersections was constructed from the data set. The topological structure of that flow was visualized by constructing a branched manifold such that every periodic orbit in the flow could be held by the branched manifold. The branched manifold, or induced template, was computed using the three lowest-period orbits. The organization of the higher-period orbits predicted by this induced template was compared with the organization of the orbits reconstructed from the data set with excellent results. The consequences of the presence of certain knots found in the data are discussed.     

A sufficient condition for self-concordance,with application to some classes of structured convex programming problems

Recently a number of papers were written that present low-complexity interior-point methods for different classes of convex programs. The goal of this article is to show that the logarithmic barrier function associated with these programs is self-concordant. Hence the polynomial complexity results for these convex programs can be derived from the theory of Nesterov and Nemirovsky on self-concordant barrier functions. We also show that the approach can be applied to some other known classes of convex programs.This author's research was supported by a research grant from SHELL.On leave from the Eötvös University, Budapest, Hungary. This author's research was partially supported by OTKA No. 2116.     

A locus for transnational exchanges: European mathematical journals for students and teachers, 1860s–1914

While there were a few mathematical journals aimed at teachers and students as early as the 1840s, it was only in the late 19th century that they became more numerous in Europe. This article is based on the analysis of a corpus of European mathematical journals published between the 1860s and World War I, selected in the first place because they were aimed at high school teachers and high school or/and first two years university students, which are often referred to as “intermediate journals”. All these journals had focused on the teaching of mathematics and, as such, they were shaped by the educational context of the country in which they were published. However, leafing through theses journals, one is struck by the fact that the mathematics they published was in fact highly commensurable, and can see that they were the locus of transnational exchanges on mathematical knowledge. This article shows that several aspects of “internationalisation” were in fact at stake in mathematical journals for students: making knowledge from elsewhere available and of publicizing to the whole world the mathematics produced in one country; making people from different countries collaborate. Finally, it focuses on the effects of transnational exchanges between journals for teachers and students: what was the mathematical knowledge that was circulated through them, and in what respect was it different from that published in other mathematical journals?     

基于DEA模型的中国家电上市公司效率实证分析

基于规模报酬可变的DEA模型和Malmquist指数方法,利用中国22家家电上市公司2006-2011年间的截面数据和面板数据,从静态视角和动态视角双维度考察了这一时期中国家电上市公司效率状况.研究发现,2006-2011年期间中国家电上市公司技术效率状况不佳,平均值为0.87,技术效率经历了下降后缓慢上升的趋势;中国家电上市公司动态效率较低,平均增长率为2.3%,且动态效率具有明显的波动性,缺乏持续的增长趋势,技术进步是中国家电上市公司动态效率增长主要动力,技术效率对其增长贡献较小.     

基于Vague集的二阶不确定性决策融合模型

针对广义传感器使用所产生的弱知识环境下不确定信息决策融合问题,给出了基于二阶Vague集的不确定信息的融合模型.通过数据示例演示了方法操作过程,并从不确定性来源、数据、模型、性能等方面讨论了本算法的先进性.结果表明,方法在二阶不确定决策融合中具有准确度高、稳定性好、容错能力强等优点.     

Proof validation in real analysis: Inferring and checking warrants

In the study reported here, we investigate the skills needed to validate a proof in real analysis, i.e., to determine whether a proof is valid. We first argue that when one is validating a proof, it is not sufficient to make certain that each statement in the argument is true. One must also check that there is good reason to believe that each statement follows from the preceding statements or from other accepted knowledge, i.e., that there is a valid warrant for making that statement in the context of this argument. We then report an exploratory study in which we investigated the behavior of 13 undergraduates when they were asked to determine whether or not a particular flawed mathematical argument is a valid mathematical proof. The last line of this purported proof was true, but did not follow legitimately from the earlier assertions in the proof. Our findings were that only six of these undergraduates recognized that this argument was invalid and only two did so for legitimate mathematical reasons. On a more positive note, when asked to consider whether the last line of the proof followed from previous assertions, a total of 10 students concluded that the statement did not and rejected the proof as invalid.     

北京市水资源利用建模分析研究

以北京市为例,分别应用无偏灰色GM(1,1)模型和非线性模型对北京市2001年-2010年的用水量进行了建模,利用最优化方法,计算了上述两种模型的最优组合模型,通过三种模型分别计算了北京市2001年-2010年的水资源利用量,并与北京市2001年-2010年的实际用水量进行了对比,采用精度检验方法,分别对无偏灰色模型,非线性模型和组合模型进行了精度检验,计算结果表明,加权组合模型是三种模型中精度最高的模型,通过组合模型计算得出的用水量值与实际水资源利用量相比误差最小,由此得出,可以利用组合模型对北京市未来的水资源利用量进行预测,预测结果可为其他相关研究提供参考.     

Evaluating nonlinear variability of mental fatigue behavioral indices during long‐term attentive task

This study investigates the behavioral indices of attention. A simple repetitive attentive task that resulted in mental fatigue was used consecutively in four trials. In the first step, reaction time and error responses were recorded to evaluate differences among trials. During the task, subjects showed different responses to stimulations. In the second part, to recognize the strategies, multiple clustering methods such as k‐means and fuzzy c‐means were performed in which behavioral indices and nonlinear features were used. In the last section, mental behavior was identified as a result of the chaotic properties of variations in reaction time. Therefore, the Lyapunov exponent of reaction times was evaluated. Results revealed that behavioral indices could distinguish attention from the occurrence of mental fatigue in trials. In addition, the three strategies used by subjects during the test protocol were assessed. Finally, variation of indices extracted from nonlinear analysis, that is, decrease in degree of chaotic behavior determined the transition from attention to mental fatigue. © 2012 Wiley Periodicals, Inc. Complexity, 2012